Question: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $t \neq 0$. $z = \dfrac{4}{3t^2 - 6t} \div \dfrac{4}{10(t - 2)} $
Dividing by an expression is the same as multiplying by its inverse. $z = \dfrac{4}{3t^2 - 6t} \times \dfrac{10(t - 2)}{4} $ When multiplying fractions, we multiply the numerators and the denominators. $z = \dfrac{ 4 \times 10(t - 2) } { (3t^2 - 6t) \times 4 } $ $ z = \dfrac {4 \times 10(t - 2)} {4 \times 3t(t - 2)} $ $ z = \dfrac{40(t - 2)}{12t(t - 2)} $ We can cancel the $t - 2$ so long as $t - 2 \neq 0$ Therefore $t \neq 2$ $z = \dfrac{40 \cancel{(t - 2})}{12t \cancel{(t - 2)}} = \dfrac{40}{12t} = \dfrac{10}{3t} $